It is given that acceleration is constant, so can we infer that average speed and velocity are the same?? Moreover, circular motion is out of the question, as the function of x(t) where x=displacement, suggests, that for any t>=0, displacement can not be zero…

This is the conceptual problem I am facing in a question:

My teacher was reading out the question, and it was asked only to find the avg velocity from the acceleration. She, on her own, added a part to it, asking us to also find avg speed, and then, while discussing solutions, said that a graph must be made in order to solve this…so do you think that it is absolutely necessary? Moreover, if my premise is flawed, then how can the graph even help??

Thanks in advance!

## Best Answer

Let's see with help of an example.

Let the particle is at $(0,0)$ moving with speed of $2m/s$ at $t=0$ and is subjected to acceleration $-2\hat i\ \text{m/s}^{-2}$.Now see after $2 seconds$.

We see displacement is zero,and distance travelled =$2m$ .Also acceleration is constant but still $\langle speed\rangle\not=0$ whereas $\langle velocity \rangle=0$

Now let's see the graphs for this scenario.

You see distance traveled is area under v-t curve (all positive) but displacement is are with signs. The area under X-axis is negative.

So, graphs can help in cases where velocity changes direction.